Hongmei Li

By absorbing large amounts of anthropogenic carbon from the atmosphere, the ocean strongly buffers the magnitude of warming caused by CO₂ emissions. This ocean carbon uptake is often conceptually separated into two components, quantified by the feedback parameters β and γ: The uptake of anthropogenic CO₂ driven by rising atmospheric concentration (β), and the effect of climate warming (γ), which reduces this anthropogenic uptake and drives a loss of natural carbon already stored in the ocean. Together, β and γ determine how effectively the ocean absorbs CO₂ emissions and shape how much emitted carbon remains in the atmosphere. Thus, β and γ directly affect how much the climate system warms in response to emitted carbon, i.e., the transient climate response to cumulative CO₂ emissions (TCRE). However, estimates of ocean β and γ from Earth system models differ widely, leading to substantial uncertainty in the TCRE. Here, we extend and apply a previously identified emergent constraint linking ocean anthropogenic carbon uptake to observable indicators of the formation of Southern Ocean mode and intermediate waters, North Atlantic deep water formation, and the global surface ocean chemical uptake capacity. In addition to these three predictors, we add an additional indicator for bottom water formation via open-ocean deep convection, defined as the volume of waters below 3000 m that is ventilated via extremely deep mixed layer depths. Using observations of these four indicators, the constrained β is 0.96±0.05 Pg C ppm−1 at doubling of atmospheric CO₂ and 0.85±0.04 Pg C ppm−1 at quadrupling of atmospheric CO₂. The observationally constrained β is around 4-5% larger and around 35-47% less uncertain than previously estimated. This larger ocean β is further supported by simulated historical anthropogenic carbon uptake in most models being lower than observation-based estimates, although uncertainties in the latter remain too large to directly constrain β. Beyond constraining ocean β, we show that ocean β and γ become increasingly correlated over time. This relationship emerges because models with higher anthropogenic carbon uptake, and hence larger β, also show a stronger suppression of that uptake in response to climate change. The stronger suppression is driven by a larger reduction in the indicators for ocean carbon uptake identified above in models with higher indicators at the beginning of the simulations, e.g., a model with stronger ventilation at present will also see a stronger reduction of that ventilation in the future. As atmospheric CO₂ increases, the climate-driven reduction in anthropogenic carbon uptake increasingly dominates over the climate-driven loss of natural carbon, causing γ to become primarily controlled by reductions in anthropogenic carbon uptake over time. As a result, the same observable indicators that constrain ocean β also constrain ocean γ at high CO₂. At doubling of atmospheric CO₂, this yields a constrained ocean γ of -10.1±2.4 Pg C ◦C−1, which is 23% larger in magnitude but has the same uncertainty as the unconstrained multi-model mean. Reflecting the strengthening of this relationship with increasing atmospheric CO₂, the constraint tightens further at quadrupling of CO₂ to -24.5±3.6 Pg C °C−1, which is 28% larger and 42% less uncertain. Overall, we have extended a previous constraint for the ocean carbon uptake by (1) adding an additional parameter that removed a known bias from unrealistic open-ocean deep convection, (2) transferring the constraint to γ and providing a mechanistical explanation for that constraint and evidence for that mechanism, (3) applying the constraint regionally, (4) identifying substantial biases in β and γ and reducing uncertainties, and (5) improving process understanding of drivers of changes in the ocean carbon sink. Although both the increase in atmospheric CO₂ uptake and the increase in carbon loss with climate change were biased across the model ensembles and could be constrained, the bias corrections of β and γ offset each other, leaving the best estimate of the ocean carbon sink relatively unchanged (2–3% increase compared to this ensemble mean). However, the uncertainties of β and γ are reduced and hence is the overall uncertainty of the carbon sink, which will propagate into smaller uncertainties of important climate metrics such as the TCRE.

We examine the behavior of ten Earth system models under a set of idealized CO2 emissions-driven simulations to look at regional temperature and precipitation changes in response to either an abrupt cessation of emissions or an idealized exceedance-and-return pathway, in which emissions linearly ramp down from positive to negative emissions. This allows a comparison of the regional climate at three different time points, all of which have the same level of cumulative CO2 emissions and therefore the same expected global warming amount. I.e., this lets us ask how regional climates would differ if we first emit, and then remove, a given amount of CO2, as compared to a case where the CO2 past a certain amount hadn't been emitted, and the coupled carbon-climate system had been left to freely evolve over the same length of time. We find consistently higher global precipitation for a given global temperature after zero emissions in both pathways, with a larger increase under the exceedance-and-return pathway than the zero-emissions pathway. Averaging over land and ocean domains, we find cooling over land relative to ocean, which is also stronger under exceedance-and-return than zero-emissions, and for about half of the models a difference in the relationship between land-ocean temperature contrast and global mean temperature change than occurs under positive emissions. We find low agreement across different models in the regional patterns of both temperature and precipitation change in all scenarios. For most of the models, there is a strong gridcell-level correlation between the temperature changes in the exceedance-and-return and zero-emissions responses, such that roughly half of the regional variance in temperature change at a given location that occurs under the exceedance-and-return pathway also occurs under zero emissions. Because only a single realisation of each experiment is available, this shared fraction is a lower bound on the common forced response: internal variability, which is uncorrelated between the two experiments, acts to reduce the apparent correspondence rather than inflate it. However, for some models there is low or negative correlation between the regional climate changes in the two cases, indicating a potential for fundamentally different regional climate change under exceedance-and-return than under zero emissions. Regional precipitation changes are more different between the exceedance-and-return and zero-emissions responses for all models.

By absorbing large amounts of anthropogenic carbon from the atmosphere, the ocean strongly buffers the magnitude of warming caused by CO2 emissions. This ocean carbon uptake is often conceptually separated into two components, quantified by the feedback parameters β and γ: The uptake of anthropogenic CO2 driven by rising atmospheric concentration (β), and the effect of climate warming (γ), which reduces this anthropogenic uptake and drives a loss of natural carbon already stored in the ocean. Together, β and γ determine how effectively the ocean absorbs CO2 emissions and shape how much emitted carbon remains in the atmosphere. Thus, β and γ directly affect how much the climate system warms in response to emitted carbon, i.e., the transient climate response to cumulative CO2 emissions (TCRE). However, estimates of ocean β and γ from Earth system models differ widely, leading to substantial uncertainty in the TCRE. Here, we extend and apply a previously identified emergent constraint linking ocean anthropogenic carbon uptake to observable indicators of the formation of Southern Ocean mode and intermediate waters, North Atlantic deep water formation, and the global surface ocean chemical uptake capacity. In addition to these three predictors, we add an additional indicator for bottom water formation via open-ocean deep convection, defined as the volume of waters below 3000 m that is ventilated via extremely deep mixed layer depths. Using observations of these four indicators, the constrained β is 0.96±0.05 Pg C ppm−1 at doubling of atmospheric CO2 and 0.85±0.04 Pg C ppm−1 at quadrupling of atmospheric CO2. The observationally constrained β is around 4-5% larger and around 35-47% less uncertain than previously estimated. This larger ocean β is further supported by simulated historical anthropogenic carbon uptake in most models being lower than observation-based estimates,although uncertainties in the latter remain too large to directly constrain β. Beyond constraining ocean β, we show that ocean β and γ become increasingly correlated over time. This relationship emerges because models with higher anthropogenic carbon uptake, and hence larger β, also show a stronger suppression of that uptake in response to climate change. The stronger suppression is driven by a larger reduction in the indicators for ocean carbon uptake identified above in models with higher indicators at the beginning of the simulations, e.g., a model with stronger ventilation at present will also see a stronger reduction of that ventilation in the future. As atmospheric CO2 increases, the climate-driven reduction in anthropogenic carbon uptake increasingly dominates over the climate-driven loss of natural carbon, causing γ to become primarily controlled by reductions in anthropogenic carbon uptake over time. As a result, the same observable indicators that constrain ocean β also constrain ocean γ at high CO2. At doubling of atmospheric CO2, this yields a constrained ocean γ of -10.1±2.4 Pg C ◦C−1, which is 23% larger in magnitude but has the same uncertainty asthe unconstrained multi-model mean. Reflecting the strengthening of this relationship with increasing atmospheric CO2, the constraint tightens further at quadrupling of CO2 to -24.5±3.6 Pg C °C−1, which is 28% larger and 42% less uncertain. Overall, we have extended a previous constraint for the ocean carbon uptake by (1) adding an additional parameter that removed a known bias from unrealistic open-ocean deep convection, (2) transferring the constraint to γ and providing a mechanistical explanation for that constraint and evidence for that mechanism, (3) applying the constraint regionally, (4) identifying substantial biases in β and γ and reducing uncertainties, and (5) improving process understanding of drivers of changes in the ocean carbon sink. Although both the increase in atmospheric CO2 uptake and the increase in carbon loss with climate change were biased across the model ensembles and could be constrained, the bias corrections of β and γ offset each other, leaving the best estimate of the ocean carbon sink relatively unchanged (2–3% increase compared to this ensemble mean). However, the uncertainties of β and γ are reduced and hence is the overall uncertainty of the carbon sink, which will propagate into smaller uncertainties of important climate metrics such as the TCRE.

Marine heatwaves (MHWs) perturb air–sea CO ₂ fluxes, but their cumulative impact on the global coastal carbon sink remains poorly understood. Using four observation-based CO ₂ flux datasets, with priority given to a global coastal product, we find that MHWs enhance net CO ₂ uptake in global shelf seas by 11.0 ± 1.6% from 1985 to 2020, in contrast to reduced uptake in the open ocean. The enhancement is largely attributable to polar and subpolar shelf seas, where frequent MHWs coincide with sea-ice loss and non-thermal reductions in dissolved inorganic carbon (DIC), outweighing reduced uptake or enhanced outgassing in lower-latitude, warming-dominated regions. Analysis with a global ocean biogeochemical model suggests that the observed DIC reductions are largely linked to enhanced biological carbon fixation. Our findings reveal region-specific MHW impacts on coastal carbon dynamics, highlighting a critical role of high-latitude shelf systems in the global carbon budget under ongoing climate change.

The Zero Emissions Commitment (ZEC), the residual warming after anthropogenic CO₂ emissions cease, remains poorly constrained and directly affects remaining carbon budget calculations. We fit a simple coupled carbon-climate model to ten Earth System Models (ESMs) in the flat10 Model Intercomparison Project. Near-zero multi-model mean ZEC can be decomposed into unrealised ocean warming contributing roughly +0.2 K at 50 years post-cessation, which is almost exactly offset by ~-0.2 K of cooling from atmospheric CO₂ drawdown into land and ocean carbon sinks. Yet the thermal term carries more than twice the inter-model spread of the carbon term; as such, in the context of current ESMs, reducing ZEC uncertainty depends more strongly on equilibrium climate sensitivity and the slow ocean heat uptake timescale than on carbon-cycle parameters. Individual models split into a carbon-dominated majority (eight of ten, negative ZEC) and a thermal-dominated minority (positive ZEC), distinguished primarily by their realised warming fraction and equilibrium climate sensitivity. The simple model yields a compact analytical formula for ZEC in terms of component climate and carbon-cycle parameters, reproducing ESM-simulated values to within ~0.03 K (less than 5% of the ~0.6 K inter-model spread). The decomposition also reveals that the carbon cycle buffers ZEC against uncertainty in committed warming to an existing energetic imbalance: recent downward revisions of the realised warming fraction (the ratio of transient to equilibrium warming) imply substantially more committed warming at fixed atmospheric composition, yet this additional heat is strongly attenuated before it appears in ZEC. A reduction of 10 per cent in the realised warming fraction would increase the radiatively committed warming by ~0.5 K at cessation, but this shifts the 50-year ZEC by only ~0.05 K. This allows potential for process-level constraints on climate and carbon-cycle components on ZEC to narrow carbon budgets. Out-of-sample testing on the flat10-cdr experiment shows that CO₂ predictions diverge from ESMs within ~50 years of the emission trajectory departing from the training rate, so the framework does not extend to full climate reversibility under sustained negative emissions. Structural limitations, including under-sampled land biosphere diversity across ESMs, may further emerge at higher warming levels or on multi-centennial timescales.

The Zero Emissions Commitment (ZEC), the residual warming after anthropogenic CO₂ emissions cease, remains poorly constrained and directly affects remaining carbon budget calculations. We fit a simple coupled carbon-climate model to ten Earth System Models (ESMs) in the flat10 Model Intercomparison Project. Near-zero multi-model mean ZEC can be decomposed into unrealised ocean warming contributing roughly +0.2 K at 50 years post-cessation, which is almost exactly offset by ~-0.2 K of cooling from atmospheric CO₂ drawdown into land and ocean carbon sinks. Yet the thermal term carries more than twice the inter-model spread of the carbon term; as such, in the context of current ESMs, reducing ZEC uncertainty depends more strongly on equilibrium climate sensitivity and the slow ocean heat uptake timescale than on carbon-cycle parameters. Individual models split into a carbon-dominated majority (eight of ten, negative ZEC) and a thermal-dominated minority (positive ZEC), distinguished primarily by their realised warming fraction and equilibrium climate sensitivity. The simple model yields a compact analytical formula for ZEC in terms of component climate and carbon-cycle parameters, reproducing ESM-simulated values to within ~0.03 K (less than 5% of the ~0.6 K inter-model spread). The decomposition also reveals that the carbon cycle buffers ZEC against uncertainty in committed warming to an existing energetic imbalance: recent downward revisions of the realised warming fraction (the ratio of transient to equilibrium warming) imply substantially more committed warming at fixed atmospheric composition, yet this additional heat is strongly attenuated before it appears in ZEC. A reduction of 10 per cent in the realised warming fraction would increase the radiatively committed warming by ~0.5 K at cessation, but this shifts the 50-year ZEC by only ~0.05 K. This allows potential for process-level constraints on climate and carbon-cycle components on ZEC to narrow carbon budgets. Out-of-sample testing on the flat10-cdr experiment shows that CO₂ predictions diverge from ESMs within ~50 years of the emission trajectory departing from the training rate, so the framework does not extend to full climate reversibility under sustained negative emissions. Structural limitations, including under-sampled land biosphere diversity across ESMs, may further emerge at higher warming levels or on multi-centennial timescales.

Future climate scenario projections are usually run with prescribed atmospheric CO2 concentrations. However, by not allowing the carbon cycle to interactively respond to emissions in Earth System models, the role of carbon cycle feedbacks on contributions to differences in climate model projections may be undersampled. Here, we present the main findings of two Earth System Models (MPI-ESM1.2-LR and NorESM2-LM) run with CO2 emissions to 2300 for three scenarios, two of which are climate overshoot scenarios, that were part of the Coupled Model Intercomparison Project Phase 6 (CMIP6). These experiments serve three important purposes: (i) an increasing focus on emissions driven runs, supplementing scenarios produced for the Coupled Climate-Carbon Cycle (C4MIP) and Carbon Dioxide Removal (CDRMIP) contributions to CMIP6; (ii) a focus on overshoot scenarios; and (iii) an extension of results beyond 2100, the timescales at which some of the most significant differences play out. Of the two models, NorESM2-LM shows more asymmetry in its climate response at the same global mean temperature levels before and after peak warming, particularly in terms of its regional pattern of warming and Atlantic Meridional Overturning Circulation (AMOC) response, with a substantially weakened AMOC persisting for decades after peak warming that takes more than a century to recover. In contrast, MPI-ESM1.2-LR shows reversibility with AMOC strength and regional warming more closely following surface temperature, but with some climate signals such as sea-level rise and ocean deoxygenation essentially irreversible. This diversity in model responses highlights the need for further research with a larger model ensemble that focuses on long-term emissions-driven model runs, particularly for overshoot scenarios, for CMIP7.

Attributing atmospheric carbon dioxide (CO ₂ ) growth to anthropogenic emissions in the presence of natural climate variability, both in the past and in the near future, is critical for assessing the impact of climate policies on the Earth system toward establishing early warnings for the carbon cycle and climate extremes. Using ensemble simulations from six novel prediction systems based on Earth system models (ESMs), we investigate reconstructions and predictions of the CO ₂ fluxes and atmospheric CO ₂ growth. These systems enable predictions of atmospheric CO ₂ growth variations in response to air–sea and air–land CO ₂ fluxes via activating the interactive carbon cycle, which is missing in the conventional decadal prediction systems with prescribed atmospheric CO ₂ concentration. The reconstructions from assimilation runs, integrating physical atmosphere and ocean data products, reproduce the annual mean observed variations in the CO ₂ fluxes and atmospheric CO ₂ growth to a large degree. The emission-driven prediction systems show predictive skill for up to 2 years for the air–land CO ₂ fluxes and atmospheric CO ₂ growth, while the air–sea CO ₂ fluxes have higher skill for up to 5 years, indicating that the predictive skill of atmospheric CO ₂ growth is limited by the air–land CO ₂ fluxes. While predictions of air–land CO ₂ fluxes are linearly linked to El Niño–Southern Oscillation (ENSO), predictions of air–sea CO ₂ fluxes are less so. The ESMs’ ability to predict variations in CO ₂ fluxes regardless of their linear relationship with ENSO merits further study of the mechanisms regulating the predictive skill toward improving our predictive capability in a closed Earth system. Significance Statement: This study aims to reconstruct variations in carbon dioxide (CO ₂ ) fluxes and atmospheric CO ₂ growth over the past decades and predict the changes in the next years. This has urgent implications for informing decarbonization and climate mitigation policy, as the global carbon cycle is affected by anthropogenic CO ₂ emissions and interacts with the changing climate. Six novel prediction systems based on Earth system models (ESMs) provide comprehensive carbon cycle estimates within a closed budget while enabling process-based attribution of the variations. We demonstrate that these initialized ESMs can predict the variations in atmospheric CO ₂ growth for 2 years. The outcomes have recently contributed to the Global Carbon Budget annual updates and the World Meteorological Organization Lead Centre for Annual-to-Decadal Climate Prediction.

The Zero Emissions Commitment (ZEC), the residual warming after anthropogenic CO₂ emissions cease, remains poorly constrained and directly affects remaining carbon budget calculations. We fit a simple coupled carbon-climate model to ten Earth System Models (ESMs) in the flat10 Model Intercomparison Project. Near-zero multi-model mean ZEC can be decomposed into unrealised ocean warming contributing roughly +0.2 K at 50 years post-cessation, which is almost exactly offset by ~-0.2 K of cooling from atmospheric CO₂ drawdown into land and ocean carbon sinks. Yet the thermal term carries more than twice the inter-model spread of the carbon term; as such, in the context of current ESMs, reducing ZEC uncertainty depends more strongly on equilibrium climate sensitivity and the slow ocean heat uptake timescale than on carbon-cycle parameters. Individual models split into a carbon-dominated majority (eight of ten, negative ZEC) and a thermal-dominated minority (positive ZEC), distinguished primarily by their realised warming fraction and equilibrium climate sensitivity. The simple model yields a compact analytical formula for ZEC in terms of component climate and carbon-cycle parameters, reproducing ESM-simulated values to within ~0.03 K (less than 5% of the ~0.6 K inter-model spread). The decomposition also reveals that the carbon cycle buffers ZEC against uncertainty in committed warming to an existing energetic imbalance: recent downward revisions of the realised warming fraction (the ratio of transient to equilibrium warming) imply substantially more committed warming at fixed atmospheric composition, yet this additional heat is strongly attenuated before it appears in ZEC. A reduction of 10 per cent in the realised warming fraction would increase the radiatively committed warming by ~0.5 K at cessation, but this shifts the 50-year ZEC by only ~0.05 K. This allows potential for process-level constraints on climate and carbon-cycle components on ZEC to narrow carbon budgets. Out-of-sample testing on the flat10-cdr experiment shows that CO₂ predictions diverge from ESMs within ~50 years of the emission trajectory departing from the training rate, so the framework does not extend to full climate reversibility under sustained negative emissions. Structural limitations, including under-sampled land biosphere diversity across ESMs, may further emerge at higher warming levels or on multi-centennial timescales.